six degrees of freedom, the topology can be laid out by resorting to qualitative reasoning.
More specifically, the paper focuses on cases whereby the manipulation tasks pertain to
displacements with the algebraic structure of a group. Besides the well-known planar and
spherical displacements, this is the case of displacements involving: rotation about a given
axis and translation in the direction of the same axis (cylindrical subgroup); translation in two …